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Covariates in CBC/HB

Dear All,

I have a rather basic question. What is the benefit of using covariates in CBC/HB instead of estimating the utilities for each subpopulation individually? Illustrative example: Imagine I want to use gender as covariate and I have a sample size in each gender split that would allow to do the estimation for males and females separately. What is the difference between using covariates and doing the analysis for the subgroups?
From my experience differences between groups are higher if you estimate the utilities for each subpopulation separately compared to using covariates. Is this higher difference "Noise" which is corrected for when using covariates?

The big difference is that that Covariates model is more parsimonious, because you are only estimating a single covariance matrix for the entire population. But, when you separate as two HB runs by gender, you are estimating a covariance matrix separately for each subgroup.

My opinion is that evenly poorly chosen covariates should have minimal negative impact on subsequent market simulation predictions. But, I'm basing that on discussions I've had with Peter Lenk, who is much more experienced in this area. My recollection of our discussion is that he is of the opinion that covariates are very robust to misspecification and misuse. He says you can pretty much throw the "kitchen sink" into it (most any variable you want) and the results are very robust to useless covariates. I don't know if this is true in most every instance, but Peter certainly has experience.

1 Answer

+5 votes

When using covariates, you are not estimating the groups separately. Rather you are simply informing the upper (population) model that there are two subgroups (male and female). All the respondents are still estimating together, and they are still using HB's power to strengthen each other. If you estimate the subgroups separately, you do not get the influence from the other subgroups.

"Which way is better" is a subjective question. If you believe that male preferences are not entirely disconnected from female preferences, you may decide to run the analysis with covariates. If you believe they are separate entities, you may want to run them separately.

We have discovered that when using covariates, you should be cautious about what covariates are chosen. Gender may not be a significant predictor of choice, and so using it as a covariate will not be helpful and possibly harmful. You should choose covariates that have significance in terms of choice prediciton.